In organic chemistry, Möbius aromaticity is a special type of aromaticity believed to exist in a number of organic molecules. In terms of MO theory these compounds have in common a monocyclic array of molecular orbitals in which there is an odd number of out-of-phase overlaps which reveals the opposite pattern of aromatic character to Hückel systems. The spatial configuration of the orbitals is reminiscent of a Möbius strip hence the name. The smallest member of this class of compounds would be trans-benzene. Möbius aromaticity was predicted in 1964 by Heilbronner by application of the Hückel method  but the first practical compound was synthesized in 2003 by the group of Herges 
The compound (6 in the image below) was synthesized in several photochemical cycloaddition reactions from tetradehydrodianthracene 1 and the ladderane syn-tricyclooctadiene 2 as a substitute for cyclooctatetraene .
Intermediate 5 was a mixture of 2 isomers and the final product 6 a mixture of 5 isomers with different cis and trans configurations. One of them was found to have a C2 molecular symmetry corresponding to a Möbius aromat and another Hückel isomer was found with Cs symmetry. Despite having 16 electrons in its pi system (making it a 4n antiaromatic compound) the Heilbronner prediction was borne out because according to Herges the Möbius compound was found to have aromatic properties. With bond lengths deduced from X-ray crystallography a HOMA value was obtained of 0.50 (for the polyene part alone) and 0.35 for the whole compound which qualifies it as a moderate aromat.
The difference was demonstrated in a hypothetical pericyclic ring opening reaction to cyclododecahexaene. The Hückel TS (left) involves 6 electrons (arrow pushing in red) with Cs molecular symmetry conserved throughout the reaction. The ring opening is disrotatory and suprafacial and both bond length alternation and NICS values indicate that the 6 membered ring is aromatic. The Möbius TS with 8 electrons on the other hand has lower computed activation energy and is characterized by C2 symmetry, a conrotatory and anatarafacial ring opening and 8-membered ring aromaticity.
Another interesting system is the cyclononatetraenyl cation explored for over 30 years by Paul v. R. Schleyer et al. This reactive intermediate is implied in the solvolysis of the bicyclic chloride 9-deutero-9'-chlorobicyclo[6.1.0]-nonatriene 1 to the indene dihydroindenol 4  . The starting chloride is deuterated in only one position but in the final product deuterium is distributed at every available possition. This observation is explained by invoking a twisted 8-electron cyclononatetraenyl cation 2 for which a NICS value of -13.4 (outsmarting benzene) is calculated .
In 2005 the same v. R. Schleyer  questioned the 2003 Herges claim: he analyzed the same crystallographic data and concluded that there was indeed a large degree of bond length alternation resulting in a HOMA value of -0.02, a computed NICS value of -3.4 ppm also did not point towards aromaticity and (also inferred from a computer model) steric strain would prevent effective pi-orbital overlap.
- Hckel molecular orbitals of Möbius-type conformations of annulenes Tetrahedron Letters, Volume 5, Issue 29, 1964, Pages 1923-1928 E. Heilbronner
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- Note that the Möbius ring is formed in formal metathesis reaction between 1 and COT
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- Investigation of a Putative Möbius Aromatic Hydrocarbon. The Effect of Benzannelation on Möbius [4n]Annulene Aromaticity Castro, C.; Chen, Z.; Wannere, C. S.; Jiao, H.; Karney, W. L.; Mauksch, M.; Puchta, R.; Hommes, N. J. R. v. E.; Schleyer, P. v. R. J. Am. Chem. Soc.; (Article); 2005; 127(8); 2425-2432. doi:10.1021/ja0458165